I have to agree that these are two instances in the novel that, at first glance, don't seem to have very much in common. However, one point of comparison between the two lies in the fact that who people appear to be on the surface is not always who they really are underneath. I think a lesson that Scout and Jem learn from this is that you can't make assumptions about people and expect them to be unequivocally true. This lesson serves them well later in the piece (or at least serves Scout well) with regard to understanding Boo.

Here is where I see the most direct comparison between the two incidents. Atticus hides the fact that he is an excellent shot because this is not something that he is really all that proud of (shooting is a last resort for emergencies in Atticus' viewpoint). It is not a character trait he feels his children need to emulate, but he is courageous enough to do what must be done. What Jem and Scout learn about courage from this scene is that true courage is silent. It comes out when the time is right, when it is needed. It is not something that you need to brag about, nor is it something that you should ever have want to have to use.

Ms. Dubose, too, has a hidden self - the struggling addict who is to be both admired for her strength and understood for her suffering. She does not want pity, even though her desire to hide her weakness makes her appear to be a mean old lady. Jem learns to view her differently when he sees the truth and the pain that she suffers. He learns that sometimes there is courage in just surviving.

I never considered a relationship between Atticus' shooting accuracy and Mrs. Dubose's morphine addiction before, but I suppose there are some comparisons to be made. Atticus is apparentlly not very proud of his old nickname, "One-Shot Finch," and he has done his best to live it down through the years. He never bothered to tell his children; he doesn't own a gun nor did he buy one for Jem; and he didn't want to take the shot on the rabid Tim Johnson until the rifle was literally thrust upon him by Sheriff Tate. To Atticus, being good at shooting is the same as being good at killing, and this trait was not to his liking, so he gave it up.

Being a morphine addict was not to Mrs. Dubose's liking, either, so she, too, decided to rid herself of this habit. It may have been a bit harder for Mrs. Dubose to kick her addiction cold turkey than it was for Atticus to give up shooting, but both of these activities must have had their grip on the two neighbors.

I suppose that you could say that their definition of courage changes from being based on physical accomplishments to mental ones.  In Chapter 10, they admire the ability to shoot, which is a physical accomplishment.  By the end of Chapter 11, they are starting to admire the ability to put your mind to controlling your impulses -- as Mrs. Dubose is controlling her impulse to take morphine.

I guess that's how I see the two things being similar.  In both cases, someone has been controlling their impulses.  Atticus presumably liked to shoot and had been controlling this impulse for 30 years.  But then when the mad dog came, he had to control his impulse not to shoot (he had to know when to let his desire to shoot out for a bit).  This is similar to how Mrs. Dubose is having to control her cravings.